3. I have noticed that many Jews rock back and forth while praying;
can you explain to me why?

I also have noticed that many Jews rock back and forth when they pray
(and even when they study the law). This rocking movement is called shokelin in Yiddish.

It has been explained in various ways. The Talmud (the most important
literary work of the so called ‘oral torah’, which contains all the Jewish
traditions and which is considered holy by the Orthodox Jews) suggests that
it is an expression of ecstasy which brings to our mind the following passage
of the Psalms: “All my bones shall say, Lord, who is like unto thee….?”
(Psalm 35:10). The Jewish mystics (that is, those who study the Kabalah) have
interpreted this bodily movement as the reflection of the flickering light of
the Jewish soul, as a spark which comes from the holy light of God and has
fellowship with its source.

The Jewish philosopher Judah Halevi (1075-1141) gave an explanation of
it which is more practical, that is, it was due to the lack of prayer books
which forced people to push forward (in order to read) and backward (in order
to let the others read in their turn).

It has been said that rocking back and forth helps to inflame the
heart with devotion to God, or that it helps to banish the profane thoughts
which come into the head during prayer; or that it represents the union
between man and God, or that it helps to keep people awake, or that it is a
remnant of the times when the Jews were nomadic and would rock back and forth
upon their camels; or that it is a helpful bodily exercise to the scholars who
spend most of their time in the seated position). From time to time some leading
rabbis opposed the custom of rocking back and forth during prayers because
they considered it a lack of reverence toward God, yet this custom has
survived in the traditional communities in spite of these contrary voices.
Prayers are said without any evident bodily movement only in the Reformed and
Conservative congregations.